1. Alessandro Buzzatti Università degli Studi di Torino / SLAC
Gamma-ray Large Area
Space Telescope
OVERVIEW OF A 3C279’s FLARE
and
SIMULATION OF AGNs
Alessandro Buzzatti Università degli Studi di Torino / SLAC

2. Outline Overview of 3C279 flare in 1996 (Wehrle et al 1996)
Emission Models
LAT Simulation of 3C279 flare
Introduction to the method
Data Analysis
Tutorial
Results and Discussion
Features of the Likelihood analysis
Summary

3. Multiwavelength Light Curve
Gamma rays
flare: High amplitude of the peak
- factor of 10
High variability
- increase of 2.6 in 8h
preflare: no real variability
- 30% from chi-squared
Strong relativistic beaming
> 100 MeV
g - rays
X - rays
High correlation with gamma rays
Lower amplitude
No time lag
- within resolution time (1 day)
Same emission region of gamma rays
2 keV
X - rays
2600 A
Optical - UV
Optical - UV
Possible correlation with gamma rays
Very small amplitude
Time lag of 2-3 days
Possible constraints on emission models
R band
From Wehrle et al. 1996

4. Spectral Energy Distribution
RADIO IR UV X-RAYS GAMMA-RAYS
The variability amplitude decreases with the decreasing of the energy
The high energy spectrum is harder at the flare peak then at the preflare
The submillimeter spectral slope during the flare is the same as the X-rays to MeV spectrum
SYNCHROTRON
INVERSECOMPTON
From Wehrle et al. 1996
The ratio of the peak fluxes of the inverse Compton distribution to the synchrotron distribution gives constraints to the models that explain the provenience of the seed photons.
– The ratio here is more than quadratic.

5. Modeling Emission Processes
Ballot et al ApJ, 567, (2002)
total
accretion
disk
external
Compton
(mostly BLR)
SSC
Inverse Compton emission models:
Synchrotron Self Compton (SSC)
External Compton
Mirror Model (BLR)
synchrotron

6. External Model: BLR as a mirror
Ghisellini and Madau MNRAS 280, (1996)
Interaction with gas clouds (BLR) can change the SED
Clouds act as “mirror” for photons which are scattered into the jet
Jet can also interact directly with clouds
Wehrle et al (1996)

7. Emission Models
Assumption: single active blob in the jet is responsible for the variability
Synchrotron Self Compton (SSC)
Larger variations in synchrotron emission then inverse Compton;
Energy densities of seed photons and scattering electrons vary in phase;
In a one-zone model, the ratio is quadratic.
Contribution of photons from different emission zones and lack of data close to the gamma ray
peak don’t let us to rule out the SSC model.
External Compton (EC)
The seed photons are external and independent of the jet
The ratio is linear for changes in the electron spectrum
It could be more than linear if the bulk Lorenz factor varies together with the electron spectrum
The entire emission region cannot accelerate and decelerate over such rapid timescales

8. Simulation of the flare
We do not know yet what is the best model to explain the 3C279 emission
Need more data in the SED

9. Overview of Data Analysis
Source Model
Light curve (sliced in time bins)
Energy spectrum (per bin)
Simulated Counts Map
Function of time, energy and position
Measured Energy Spectrum
per arbitrary time bin
Reconstructed Light Curve
from integration of Energy spectra
SIMULATION
Response Function
Orbital Period
LAT
LIKELIHOOD
SOURCE MODEL
- Broken Power Law
- Power Law ok
RESULTS

10. Source Model : flaring AGN
The most flexible model is the Spectral Transient:
Calculation Steps
Define simulation time and overall average flux;
choice of parameters is arbitrary
Specify different time intervals
each of them with a proper flux and
constant energy spectrum;
Just an illustration…
Energy Spectrum of a single time bin
Broken Power Law
Index1 ok
Spectral
break
Index2

11. Input to the source model (3C279)
SOURCE MODEL PARAMETERS
Simulation time: 10 days
Average Flux: photons /cm2 /s
Energy range: 20 MeV to 200 GeV
l b 57.03
1st bin
2nd bin
3rd bin
Time
[days] 5 3 2
Relative Flux 10 1
Index1
1.7
1.5
2.1
Index2
2.5
2.2
Energy Break
[MeV]
300
1000
Consider changing the average flux
Simple template
3 time bins

12. The simulated Counts map
– integrated over time and energy
– the colors represent the counts ok
EGRET used binned Poisson Likelihood (in position space)
We use the unbinned likelihood
- each event effectively has its own response function
It will be analyzed with the likelihood test…

13. Likelihood Calculation (1)
The unbinned likelihood test is a way to compare measured counts (from a source) with predicted counts (from a model). I use the ScienceTools v5r6.
…we start from the measured counts.
STEP 1: SELECTION
slice the acquisition time ( = simulation time) into intervals of constant energy spectrum and flux.
DON’T CONFUSE WITH THE BINS USED IN THE SIMULATION!!
define a region that can contribute to the signal (Source Region)
select the portion of sky to study
(Region Of Interest) SR
ROI
STEP 2: MODELING
Create a model of the sources in the ROI (in our case, just one point source)
point sources background diffuse sources
spectral part spatial part
Spectral models generally used: Power Law and Broken Power Law. ok

14. Likelihood Calculation (2)
RESPONSE FUNCTION
EVENT DISTRIBUTION FUNCTION
ROI SR
STEP 3: PREDICTED EVENTS
Compute the Event Distribution Function:
*primed quantities are measured quantities
Integrate over the Region Of Interest to get the predicted number of counts:
Integrate over the Region Of Interest to get the predicted number of counts:
STEP 4: UNBINNED LIKELIHOOD
Maximize the Log-Likelihood. The sum is taken over all the events within the ROI. ok

15. Input to the Likelihood (3C279)
Selection on 3C279
Time Intervals = 1 day
Region Of Interest = 20°
Source Region = 30°
Energies = 30 MeV GeV
Response function not reliable under 30 MeV
Modeling
Broken Power Law
Index2
Break
Log L
4 INITIAL
VALUES ok

16. Automation of Data Analysis
Source Lightcurve
Time [days]
Flux
Science tools require automation…
Slice the acquisition time
Run likelihood test on each bin
use the same source model for all
Benoit’s
macro
(c++)
Energy dN __ dE
Energy dN __ dE
Energy dN __ dE
Python
macro
Compute the fluxes
propagation formula for the errors
Reconstruct the lightcurve
The text can reflect more what I do on the right
Fitted Flux - Source Lightcurve
Time [days]
Flux

17. Results for 3C279
Results are Spectral Index, Flux, Energy Break, Number of Counts
– continuous lines in the plots represent the true parameters
- INDEX 1
- INDEX 2
16000
750
4500
CHECK ALL THE DETAILS IN THE PLOTS (ERROR BARS)
Expected Counts per Day (averaged over each step)
– represent the statistics
The error bars on the flux are propagated without the covariance term
– underestimated

18. Summary of the Issues FLUX
The fit of the light curve depends on the number of counts
ERROR BARS
The error bars are too big
ENERGY BREAK AND INDICES
The likelihood cannot converge to the right energy break value
The indices and the energy break are strongly correlated ok

19. Dependencies on Average Flux
Same Parameters – Different Average Flux
LOW
MEDIUM HIGH
HUGE
EXTREME
previuous one
10^-8 photons /cm^2 /s
LOW 80
300 15
HIGH
800
3000
150
EXTREME
7700
27000
1100 ok
Counts < scattered
Counts ~ GOOD!
Counts > underestimated

20. Understanding the uncertainties
Poisson distribution for counts
We want sigma/flux to be as closest as possible to √N/N
one order of magnitude!
quantities are averaged on the first-step points and plotted for each run
Compare to simple Power Law spectral model
expect more precision
New source
Constant index
No Energy break
New models
Power Law Broken Power Law
- 2nd index + Break fixed

21. Comparison on Error Bars
POWER LAW
Ratio of almost one to one.
GOOD!
BROKEN POWER LAW
Discrepancy of an order of 3
Something funny is going on here…

22. Can we fit the energy break?
HUGE
The likelihood test gives back the same value used as initial input (500 MeV)
New run, with initial Break Value at 300 MeV
NEW - HUGE ok
The likelihood now gives back a value around 300 MeV
We are not able to determine the energy break

23. Correlation Energy Break – Indices
EXTREME
Strong and evident correlation
We cannot relay on the fit of the indices
Break at 300 MeV
Break at 500 MeV

24. Summary Overview of the flare of 3C279
Described multiwavelength observations
Discussed briefly possible emission models
LAT Simulation and Data Analysis with ScienceTools
Simulated a flaring AGN
Lightcurve and Energy Spectrum
Analyzed with Likelihood tools
Issues relative to the Likelihood analysis
Determination of energy break and spectral indices is not reliable for broken power law models
More investigation needed
Uncertainties is the likelihood calculations are not yet fully understood
Chi squared test is missing

25. all the summer students
Thanks to…
In order of appearance
Eduardo
Anders
Paul
Jim
Seth
Benoit
Greg
and also…
Luis
all the summer students